This study uses a genetically engineered vaccine consisting of a modified form of the vaccinia virus which has been modified to carry the gene for carcinoembryonic antigen (CEA), protein present on the surface of many adenocarcinoma cells. This recombinant vaccinia-CEA vaccine is investigational. Vaccination with the modified smallpox vaccine stimulates a potent immunologic response that is protective against the smallpox virus. The aim of this study using the recombinant vaccinia-CEA vaccine is to induce the immune system to generate a strong immune response against CEA. We hope the immune system will respond to the vaccine and mount an anti-CEA response just as it mounts a potent anti-smallpox immune response. This genetically engineered vaccine has been tested in animals and found to be safe and effective. A different production lot of this vaccine has been administered to colorectal cancer patients by scarification with no significant side effects. The vaccination program consists of two separate vaccinations four weeks apart using one or the other immunization technique (needle or jet injection). Following the first and second vaccination, patients will be monitored for any side effects. Blood samples will be drawn at various times for one month after each vaccination to monitor the immune response. Depending upon a process of random assignment, the patient may receive the vaccine by either needle injection into the skin or jet injection into tissues immediately below the skin.